Q60 of 93 Page 6

In figure, bisectors GM and HL of alternate angles AGH and DHG respectively are parallel to each other. Prove that AB || CD.
                  

GM and HL are parallel lines.
EGHF is a transversal.
     ∠MGH = ∠GHL …………………….(i)
⇒ 2∠MGH = 2∠GHL
⇒ ∠MGH + ∠AGM = ∠GHL + ∠LHD
∴ ∠AGH = ∠DHG
∴ AB and CD are two lines and EGHF is a transversal, if one pair of alternate angles are equal, the lines AB and CD are parallel.

More from this chapter

All 93 →
58 In figure, EF is a transversal to two parallel lines AB and CD. GM ad HL are the bisectors of the corresponding angles EGB and EHD. Prove that GM||HL.
                   59 If two parallel lines are intersected by a transversal, then prove that the bisectors of any two alternate angles are parallel.
                           61 If two lines are intersected by a transversal in such a way that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.
                   62 A transversal intersects two given lines in such a way that the interior angles on the same side of  the transversal are equal. Is it always true that the given lines are parallel? If not, state the condition (s) under which the two lines will be parallel.